1. simple trig

find all the values of a in the range 0 deg to 360 deg satisfying 2sina = 3cosa

i know its simple but just cant remember how to do it

2. do i just divide sin and cos for tan?

3. Hello djmccabie
Originally Posted by djmccabie
find all the values of a in the range 0 deg to 360 deg satisfying 2sina = 3cosa

i know its simple but just cant remember how to do it
Originally Posted by djmccabie
do i just divide sin and cos for tan?
Yes, you do, but remember that you must make sure that what you're dividing by is not zero. So you need to say:

$\displaystyle 2\sin a = 3\cos a$

$\displaystyle \Rightarrow 2\tan a = 3$, provided $\displaystyle \cos a \ne 0$

Then check that $\displaystyle \cos a = 0$ does not give any valid solutions and proceed with

$\displaystyle \Rightarrow \tan a = 1.5$

4. Originally Posted by djmccabie
do i just divide sin and cos for tan?
Hi dj,

Yep, pretty much.

$\displaystyle 2 \sin a = 3 \cos a$

$\displaystyle \frac{\sin a}{\cos a}=\frac{3}{2}$

$\displaystyle \tan a = \frac{3}{2}$

Now, can you find the two angles that satisfy the original equation?